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A smooth track in the form of a quarter-circle of radius $6 m$ lies in the vertical plane. A ring of weight $4 N$ moves from $P_{1}$ and $P_{2}$ under the action of forces $F_{1}, F_{2} a n d F_{3}$ . Force $F_{1}$ is always towards $P_{2}$ 20 N in magnitude; force $F_{2}$ always acts horizontally and is always $30 N$ in magnitude; force $F_{3}$ always acts tangentially to the track and is of magnitude $15 -$ $10 s$ ) $N$ where s is in distance covered meter. If the particle has speed $4 m s^{- 1}$ at $P_{1}$ what will its speed be at $P_{2}$ ?

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Important Questions on Work, Energy and Power

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A person of mass

M

is sitting on a swing of length

L

and swinging with an angular amplitude

θ_{0} .

If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance

l (l ≪ L),

is close to:

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

The velocity-time graph of a particle of mass

10 kg

is shown in the figure. The net work done on the particle in the first two seconds of the motion is

Question Image

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A bullet of mass

20 g

has an initial speed of

1 m s^{- 1}

, just before it starts penetrating a mud wall of thickness

20 c m

. If the wall offers a mean resistance of

2.5 \times 10^{- 2} N,

the speed of the bullet after emerging from the other side of the wall is close to:

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A cricket ball of mass

0.15 kg

is thrown vertically up by a bowling machine so that it rises to a maximum height of

20 m

after leaving the machine. If the part pushing the ball applies a constant force

F

on the ball and moves horizontally a distance of

0.2 m

while launching the ball, the value of

F (in N)

(g = 10 m s^{- 2})

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A force acts on a

2 kg

object so that its position is given as a function of time as

x = 3 t^{2} + 5 .

What is the work done by this force in first

5

seconds?

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

The Work - Energy theorem
(A)
(B)
(C)
(D)

HARD

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled

3 m

is:

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A bullet of mass

5 g

, travelling with a speed of

210 m s^{- 1}

strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is

0.030 {(g ° C)}^{- 1} (1 calorie = 4 .2 \times 10^{7} ergs)

close to :

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A particle which is experiencing a force, given by

\vec{F} = 3 \hat{i} - 12 \hat{j}

, undergoes a displacement of

\vec{d} = 4 \hat{i}

. If the particle had a kinetic energy of

3 J

at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

Some of the following equations are kinematical equations, where the symbols have their usual meaning. The

w o r k - e n e r g y

theorem is represented by

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A particle of charge

q

and mass

m

is subjected to an electric field

E = E_{0} (1 - a x^{2})

in the

x -

direction, where

a

and

E_{0}

are constants. Initially the particle was at rest at

x = 0

. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A body of mass

m

starts moving from rest along

x -

axis so that its velocity varies as

v = a \sqrt{s}

where

a

is a constant and

s

is the distance covered by the body. The total work done by all the forces acting on the body in the first

t

second after the start of the motion is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A small ball of mass

m

is thrown upward with velocity

u

from the ground. The ball experiences a resistive force

m k v^{2}

where

v

is its speed. The maximum height attained by the ball is :

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A running boy has the same kinetic energy as that of a man of twice his mass. If the speed of the boy is

14.14 {ms}^{- 1},

the speed of the man is

HARD

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A small block starts slipping down from a point $B$ on an inclined plane $A B$ , which is making an angle $θ$ with the horizontal section $B C$ is smooth and the remaining section $C A$ is rough with a coefficient of friction $μ$ . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $B C = 2 A C$ , the coefficient of friction is given by $μ = k tanθ$ . The value of $k$ is .......

Question Image

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

In the diagram below the spring has a force constant of $K$ , the block has a mass of $m$ , and the height of hill is $h$ . Determine the compression of the spring $x$ such that the block just reaches to the top of the hill.
(Assume that there are no non-conservative forces involved.)

Question Image

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

Which of the following statements is false?

EASY

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A body of mass

m = 1 kg

is moving in a medium and experiences a frictional force

F = - k v

, where

v

is the speed of the body. The initial speed is

v_{0} = 10 m s^{- 1}

and after

10

s, its energy becomes half of the initial energy. Then, the value of

k

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A body of mass

m = 10^{- 2} kg

is moving in a medium and experiences a frictional force

F = - k v^{2} .

Its initial speed is

v_{0} = 10 m s^{- 1} .

After

10 s

its kinetic energy is

\frac{1}{8} m v_{0}^{2},

then value of

k

will be:-

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Energy Theorem

A block of mass

10 kg

, moving in

x

direction with a constant speed of

10 m s^{- 1}

, is subjected to a retarding force

F = [(0 .1) x] J m^{- 1}

during its travel from

x = 20 m

30 m

. Its final kinetic energy will be:

Important Questions on Work, Energy and Power

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